Comparing and Ordering
Do you want to visit the candy factory in Willy Wonka and the Chocolate Factory? Just imagine all the free candy, the chocolate river, and those cheery Oompa Loompas. People who run candy factories often have to compare numbers to see what candies are the most popular.
You can compare any group of numbers, including candy sales, by using three different terms. Each of these terms comes with a special symbol:
- The symbol > means greater than
- 35 lollipops > 4 chocolates
- The symbol < means less than
- 5 hard candies < 24 gumdrops
- The symbol = means equal to
- 18 candy bars = 18 pieces of licorice
Let's imagine that we sold all of those candies. If we made a list of the candy sales in order from the smallest amount sold to the biggest amount sold, it would look like this:
4 chocolates, 5 hard candies, 18 candy bars, 18 pieces of licorice, 24 gumdrops, 35 lollipops
4, 5, 18, 18, 24, 35
These are pretty small numbers. Let's explore how to compare and order larger numbers.
Count the Digits
When comparing two or more numbers, you should first count the number of digits in each number.
Whole numbers with more digits in them are greater than numbers with fewer digits. This is because the more digits a whole number has, the more place values it includes and the larger the number becomes.
Look at the example of the total candies sold by the Willy Wonka Chocolate Factory this year.
Let's find the least popular candy by looking for the number with the least amount of digits.
Our chart says that 146 lollipops were sold. This number is 3 digits long and the other numbers have more digits, so this is our smallest number. Its largest number is in the hundreds place.
The next most popular seller is rock candy, with 23,504. This number has 5 digits, with the highest place value being the ten thousands.
Finally, the most popular seller and greatest number is gummy worms at 458,605,495. This number has 9 digits, with the highest place value being the hundred millions.
If you ordered the candy sales from greatest to least, it would be:
458,605,495 > 23,504 > 146.
Compare Place Values
What if the numbers you're comparing all have the same number of digits? If this happens, then it's time to look at the individual value of the digits in each number.
Look at the example of the number of Oompa Loompas who fell in the chocolate river over a 3-year period.
The smallest number of Ooompa Loompas that fell into the Chocolate River was 23,405 because it only has 5 digits, making its highest place value in the ten thousands. The other numbers both have 8 digits, so you have to compare the individual place values. To do this, you should:
In this example, 34,456,629 > 34,456,359 because a 6 in the hundreds place (600) is greater than a 3 in the hundreds place (300). If you ordered the number of Oompa Loompas who fell into the river from least to greatest, it would be:
23,405 < 34,456,359 < 34,456,629
With these numbers, perhaps they should hire a lifeguard!
Let's take a moment to review what we've learned.
When you compare and order numbers, you use the terms less than (<), greater than (>), and equal to (=). To compare numbers, first look at the number of digits in each number. Then, compare the place values of numbers with the same amount of digits. And now, you'll be able to order and compare numbers with no problem up to 999,999,999.
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Practice Comparing Numbers
After such a great lesson on comparing numbers, let us practice by choosing the correct answers to questions involving comparing numbers.
Which numbers are greater than 999?
(a) 1000 (b) 9999 (c) 99999 (d) 999999
All are greater, (a), (b), (c), and (d)
Which numbers are less than 999?
(a) 998 (b) 9 (c) 75 (d) 1000
(a), (b), and (c) are less
Arranging a series of numbers in ascending order is a sequence of numbers so that the one to the left is less than the one to its right. For example, 1, 2, 3, 4, 5, 6 are in ascending order. So is the sequence 1, 3, 5, 9
Which of these sequences of numbers are arranged in ascending order?
(a) 1, 3, 5, 9 (b) 2, 4, 6, 22 (c) 1, 4, 88, 999 (d) 9, 99, 999, 99999
All are in ascending order, (a), (b), (c), and (d)
Can you place the numbers, 9, 8, 7, 6, 5, 4, 3 in ascending order?
(a) 1, 2, 3, 4, 5, 6, 7, 8, 9 (b) 3, 4, 5, 6, 7, 8, 9 (c) 3, 4, 5, 6, 7, 8, 9, 10 (d) 3, 5, 4, 6, 7, 8, 9
Can you place the numbers, 3, 5, 4, 6, 8, 7, 9 in ascending order?
(a) 3, 4, 5, 6, 7,8,9 (b) 3, 5, 4, 6, 8, 7, 9 (c) 2, 3, 5, 4, 6, 8, 7, 9 (d) 3, 5, 4, 6, 8, 7, 9, 10
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